Find the dimension of the ratio of the pressure to the stress.

CONCEPT:

Pressure:

• It is defined as the normal force per unit area.
• The pressure on the surface is given as,

• Its SI unit is N/m2.
• The dimension of the pressure is given as,

⇒ [P] = [M1 L-1 T-2]

Stress:

• When an external force is applied to a material it gets deformed.
• Due to this deformation, an internal resistance force develops in the material.
• This internal resistance force per unit cross-sectional area is called stress.

Where σ = stress, P = applied load and A = cross sectional-area

• Its SI unit is N/m2.
• The dimension of the pressure is given as,

⇒ [σ] = [M1 L-1 T-2]

CALCULATION:

• The dimension of the pressure is given as,

⇒ [P] = [M1 L-1 T-2]

• The dimension of the pressure is given as,

⇒ [σ] = [M1 L-1 T-2]

So the dimension of the ratio of the pressure to the stress is given as,

• Hence, option 2 is correct.